FOM: Dawson on Aristotle

[Fred Johnson]

No doubt Dawson's *Logical Dilemmas* deserves the praise it 
has been given, but there are problems.  Unfortunately, his 
sketch of Aristotelian logic perpetuates the common myth 
that Aristotle's thoughts about logic were very primitive.

Evidence that Dawson has not read the *Prior Analytics* comes
from his claim (p. 38) that Aristotle recognized fourteen 
patterns of valid deductions.  For Darapti, which is not one
of the fourteen, Aristotle gives a valid ecthetic deduction 
that uses principles that are now commonly named UI and EG.  
The reader of *PrAn* will recognize that for Aristotle there 
are *infinitely many* valid deductions.

Dawson's claims about the lack of relevance of Aristotle's work
to "the mathemical logic of today" are irritating.  After all,
Aristotle was clear about the distinction between syntax and 
semantics.  He separated deducibility (proof theory) from 
entailment (model theory) and had his eye on soundness and 
completeness results.  

Aristotle uses second-order logic in his discussion of 
circular reasoning.  He embeds the fragmentary system 
Dawson alludes to in a developed system of modal logic that 
distinguishes two notions of possibility such that one is 
not reducible to the other.  (According to one notion, that 
it is possible that all A are B implies that it is possible
that no A are B.)  

There is no question that modern-day relevance logicians 
have made good use of Aristotle's principles.  

Fred Johnson